The core subjects of trade theory are the pattern and volume of trade: which goods are traded by which countries, and how much of those goods are traded. The first part of this paper discusses evidence on comparative advantage, with an emphasis on carefully connecting theoretical models with data analyses. The second part of the paper considers the theoretical foundations of the gravity model and reviews the small number of studies that have tried to test, rather than simply use, the implications of gravity. Both parts of the paper yield the same conclusion: we are still in the very early stages of empirically understanding specialization and the volume of trade, but the work that has been done can serve as a starting point for further research.